R. WANG and M. D. MERZ: Polymorphic Bonding and Thermal Stability 697

phys. stat. 801. (a) 39, 697 (1977)

Subject classification: 2 and 4; 1.2; 21 ; 22.1

Battelle, Pacific Northwest Laboratories, Richland')

Polymorphic Bonding and Thermal Stability of Elemental Noncrystalline Solids

BY R. WANG and M. D. MERZ

Based on a correlation found between the thermal stability of elemental noncrystalline solids and crystalline polymorphism it is suggested that the structure of noncrystalline solids is composed of atomic bonds of the crystalline polymorphs. For noncrystalline solids, each covalent element has a narrow range of stability that correlates on the basis of group number and number of poly- morphic forms. Many metallic elements, however, have a reported wide range of stability, which are divided into two characteristic ranges. The Bernal or random close-packed structure is proposed for metallic noncrystalline solids with low thermal stability whereas impurity-induced polymorphic bonding is proposed for the instances of high thermal stability.

Aufgrund von Beziehungen, die zwischen thermischer Stabilitiit von nicht-kristallinen Element- Festkorpern und kristalliner Polymorphie gefunden werden, wird vermutet, daD die Struktur nicht-kristalliner Festkorper durch die atomare Bindung des kristallinen Polymorphen bestimmt wird. Fur nicht-kristalline Festkorper hat jedes kovalente Element einen engen Stabilitiits- bereich, welcher mit der Gruppenzahl und der Zahl der polymorphen Formen in Wechselbeziehung steht. Viele Metallelemente haben jedoch einen relativ weiten Stabilitiitsbereich, der in zwei charakteristische Abschnitte eingeteilt wird. Die Bernal- oder regellos dicht gepackte Struktur wird fiir metallisch nicht-kristalline Festkorper mit geringer thermischer Stabilitiit vorgeschlagen, wiihrend die durch Verunreinigungen erzeugte polymorphe Bindung fur die Falle mit hoher ther - mischer Stabilitiit vorgeschlagen wird.

1. Introduction We have shown in a recent paper [ 11 that the occurrence of an elemental noncrystal-

line solid correlates with the number of polymorphic forms of that element and group number in the periodic table. Hence, a polymorphic bonding concept was postulated for the structure of an elemental noncrystalline solid wherein the structure is composed of a finite number of bonding states with bonding characteristics as exhibited in the crystalline polyniorphs. This implies that the short-range atomic packing and thermo- dynamics of an elemental noncrystalline solid are related to the crystalline states.

Additional evidence will be given in this paper for the existence of polymorphic bond- ing in noncrystalline solids. The thermal stability of an elemental noncrystalline solid, expressed by the reduced crystallization temperature T,, (T,, = TJT,) where T, and T, are, the crystallization and melting temperatures, respectively, correlates semi- quantitatively wit2h the polymorphism of the crystalline state. Consequently, we pro- posed a mechanism to explain the impurity-induced high stability for metallic non- crystalline solids.

2. Polymorphism and Thermal Stability The correlation of crystalline polymorphism and the thermal stability of an elemen-

tal noncrystalline solid was derived based on the plot of the number of polymorphic forms NpF of an element versus the group number N , of that element (Fig. 1). The

1) Richlend, Washington 99362, USA.

698 R. WANG and M. D. Mmz

71 t I D \ I V 081s

$ c 8 -

5 h 7 - 3 yg m I

Pu

Q 5 '\ / p , 0 7 6 !

" 6 - \ I

5 5 - 1 v = 1.033B \ 069Se I

Fig. 1. Correlation of the thermal stability of noncrystalline solids, the reduced crystalliza- tion temperature TIC, to the number of poly- morphic forms NPF and group number NG of the solid elements. The ease of formation of non-crystalline solids is illustrated by:

quenching from the liquid; A formation by vapor deposition near room temperature; by deposition at very low temperatures; @no data available; and o no known noncrystalline solid formed. The TI, values of elements are illus- trated for comparison with the calculated iso-

stability curves from equation (2)

Table 1 Thermal stabilities of covalentnon crystalline elements

0.81 0.69 0.39

~ 0 . 7 6

0.51 0.37 0.38 0.46 0.35 0.33

element

S Se Te P

As Sb C Si Ge B

0.82 0.67 0.33 0.57

0.50 0.40 0.33 0.33 0.33 0.27

320 ~ 3 1 303 to 373 [la, 151 280 r151

(673 I 3 1

555 1151 316to 352 [I51

1373 [17], 1773 [la] 773 [19,201

323 [21,22], 523 [23,24] 820 ~191

392 490 723

~ 8 3 3 (red P) 1088 903

4100 1685 1210 2498

Polymorphic Bonding and Thermal Stability of Noncrystalline Solids

Tab le 2 Thermal stabilities of metallic noncrystalline elements

699

element

Mn* *) Ni

Fe

co Cr Mo Bi Sn Ga

Zn Cd Be

Au Ag

low

80 141 34, 94 [4]

5 [28], 40 [29] 90 [30] 40 [a], 80 [4,33]

40 [34], 60 [35] 20, 25 [15]

20, 25 [15]

80 [41

*) [lo1

*) [71 *) ~361 *) ~381

*) [91 *) [391

high

400 [4] 190 [25] 345 [26] 423 [27] 180 [31] 300 [4, 321 200 [4] 200 [4]

200 [l8] 123 [36] 90 [31]

103 [37] 168 [36] 213 [36J 130 [38] 120 [40] 120 [40]

-

T d K )

1517 1726

1808

1765 2176 2888 544 505 303

693 594

1557 1234 1336

low

0.05 0.03

___.

0.02

0.03 0.04 0.01 0.04 *)

0.07

*) *) *) *) *)

high

0.26

0.20

0.17

0.11 0.09

0.37 0.24 0.3

0.24 0.36 0.08 0.1 0.1

-

T h eq. (2)

0.21

0.25

0.25

0.14 (0.1 (0.1

0.4 0.15 0.15

(0.1 (0.1 (0.1 (0.1 (0.1

*) Microcrystalline phase formed below 20 K. **) 2% impurity.

T,, values we have chosen for this study. Noticeably, for covalent elements all the T, values are greater than or equal to 0.33. However, the reported To values of the metallic elements had a much larger range, from a few K to several hundredK (Table2). We concluded that the T, values of metallic elements may be separated into two ran- ges, low stability (0.0 to 0.07) and high stability (0.1 to 0.3). I n general, high purity thin films prepared by vapor deposition in high vacuum (< Torr) have low stabil- ities: whereas thin films either with impurities or prepared in low vacuum or prepared by splat-quenching have high stabilities. Amorphous thin films of several transition metals such as Mn, Fe, Ni, Co, and Cr even show two resistivity peaks upon anneal- ing, [4] corresponding to both low and high stabilities. Table 2 shows the two ranges of T, values and the TI, values we have used in our correlation with crystalline poly- morphism and thermal stability. For reasons discussed later, the high T,, values for metallic elements best suit our correlation.

The way thermal stability varies with N , and N p g is most apparent for elements between group number 7b and 3a (Fig. 1). For elements with the same N,, higher thermal stability is found in elements with larger NpF. For those elements having the same N p F , noncrystalline solids with chain or ring structures from group 6a (S, Se, Te) are more stable than elements with layer-structures from group 5 a (As, Sb, and Bi) and more stable than elements with tetrahedral bondings from group 4a (C, Si, and Ge, etc.). Elements located outside the region between group number 7b and 3a have very low Tr, (< 0.1).

The trend of thermal stabilities for elements between group 7 b and 3a can be de- scribed by several parabola-like contours of equal T,, values with noses all located a t group 6a elements. We found that T,, for group 6a elements can be related to N p F

45 physiea (a) 39/2

700 R. WANG and M. D. M w z

by a simple equation:

According to ( l ) , S, Se, and Te (NPF are 10, 5 , and 2, respectively) have TI , values of 0.81, 0.69, and 0.33, which are very close to the reported values of 0.82,0.66, and 0.39, respectively. For elements from different groups, the effect of N , on TI, can be expres- sed surprisingly well by the relation

For constant TI , (iso-stability) (2) shows a parabolic relation between Npg and NG with minima at N , = 6. A set of parabolas of equal TIC, e.g., 0.1, 0.2, 0.33, 0.5, 0.67, and 0.82 are shown in Fig. 1 for comparison to the reported T,,. The thermal stability data of B (T,, = 0.33), C (0.38), Si (0.46)) Ge (0.35), and Sb (0.37) are very close to the calculated T,, values given by (2) and are' near the calculated contour of T , = 0.33. For As, the reported TI, value of 0.51 is close to the parabola for Tr, = 0.5; for P, the reported T,,, 0.76, is higher than the calculated T,,, 0.67. Since phosphorus has 12 poly- morphic forms, [5] we may use Npg = 12 to get T,, = 0.79 from (2). The effect of NpF on thermal stability given by (2) also agrees with the high TI, values of the metal- lic elements located between group 7 b and 8.

From the above results, it may be possible to estimate the thermal stabilities of noncrystalline phases for the other transition and semimetal elements. Thermal stabil- ities between 0.0 and 0.1 may be expected for most of the transition elements such as Cr, Mo, Pd, W, Ta, V, Nb, etc., and for semimetals such as Pb, Al, In, Zn, Cd, Ag, and Au, Fig. 1. The only reported T,, values higher than calculated from (2) are those for Ga, Sn, Zn, and Cd. Values for the transition metals Cr and Mo and the noble metals Ag and Au agree very well with the correlation.

3. Discussion The formation and stability of elemental noncrystalline solids, although complex

can be correlated somewhat simply with the basic crystalline structural forms and the group number because: (i) for each element the multiplicity of atomic bonding be- tween like atoms is expressed by the number of polymorphic forms, and (ii) the group number of the element contains information on the degree of bonding anisotropy which is also a key factor for the stability of the noncrystalline solids. We have taken this correlation as evidence for the existence of crystalline polymorphic bonding in non- crystalline solids.

So far, the polymorphic bonding concept is most successful for covalently-bonded elements in groups 6a to 3a and for the metallic elements in groups 6 b through 8 with high TI , values. However, as shown in Table 2, the thermal stability of noncrys- talline metallic elements can be low or high depending on the experimental conditions and the purity of the element. Apparently, the polymorphic bonding concept cannot explain the low stability cases where all the elements have nearly the same T,, values, less than 0.1, regardless of NG and N P F . For these cases we suspect that the low stabil- ity may be attributed to high purity and the occurrence of Bernal or random close- packed structures. Due to the flexibility of metallic bonds and the low bonding strength of metals such as Mn, Ni, Fe, and Co, the stability of the random close-packed struc- ture is very low and is easily transformedinto close-packed crystallites [6]. I n fact, high purity Fe, Cr, Ti, Mn, Co, Xi, Al, Pb, Pd, Y, Cu, Ag, Au, Sn, and Zn were reported to have formed microcrystalline phases instead of noncrystalline phases [4, 7 to 111.

Polymorphic Bonding and Thermal Stability of Noncrystalline Solids 701

Fig. 2. SchematicaI illustrations of pro- posed mechanism for impurity-induced stability of metallic noncrystalline solids. 2 Upper schematic a) shows the nearly uni- 5 form bonb formed between metallic 2 atoms in random close-packed structure .9

t and lower schematic bj shows the fluc- tuatiom of metal-metal bonds (1-2, 2-3, and 3 4 ) caused by the impurity atom $, (black) forming strong impurity-metal 2

bonds -a

9 E b v)

Thus for these low stability noncrystaline phases we would not expect a correlation with N p w .

However, the presence of impurities may disturb the bonding of an ideal random close-packed structure. The correlation we have found for the high Stability noncrys- talline metals suggests that polymorphic bonding occurs in these cases. We therefore suggest a mechanism of impurity-induced stability wherein impurity atoms have a “catalytic” effect and induce the formation of polymorphic bonding for metallic atoms.

Whenever an impurity atom (most likely one of the covalent elements) is found in the metal matrix, a number of metallic atoms will be strongly bonded to the impurity atom due to the difference in electronegativity. As a result, those impurity-bonded metal atoms will have modified bonding characteristics with neighboring metallic atoms. If traced away from the impurity-metal bond, a fluctuation of bond strength occurs as illustrated in Fig. 2. Compared with pure metallic bonding, the impurity induced bond strengths can be stabilized by forming polymorphic bondings. Accord- ingly, thermal stability is increased when a large number of different bonds are avail- able (polymorphic bonding) since a large selection of energy minima are available for structural relaxation. Thermodynamically the structure with mixed bonding is more stable than a random close-packed structure with all bonds a t nearly the same energy level.

Obviously, stability increases with impurity level and we can estimate the minimum impurity content for formation of polymorphic bonding throughout the structure. Each impurity atom that forms a bond with a neighboring metallic atom is assumed to cause fluctuations in the bonding between (i) the metal atom and its nearest neigh- bors, and (ii) these nearest neighbors and their nearest neighbors, Fig. 2. Assuming that the structure of the noncrystalline phase resembles a densely packed structure with a coordination number N , = 12 [12], a count of the number of bonds affected by one impurity atom is approximately 90 for a divalent impurity and 114 for a tetravalent impurity. Therefore, for a divalent oxygen 1/90 = 1.1 atyo will stabilize the non- crystalline phase whereas for silicon, 1/114 = 0.88 atoh is sufficient.

Based on the above mechanism, we would expect that the “catalytic” role of the impurity will be highly effective for impurity atoms substantially different in valence or electronegativity. This may explain why metal-metalloid combinations give the most stable noncrystalline phases. Also, a metallic impurity would be much less effec- tive, especially when i t has the same group number as the matrix element.

Impurity-metal bonding thus contributes to enhanced stability. When the impurity content exceeds the minimum requirement for polymorphic bonding, the polyniorphic bonds between the metallic atoms will begin to be replaced by impurity-metal bonds. Therefore, further enhancement of the stability of these noncrystalline solids should be considered an alloying effect, which will be treated in a different way. 45.

702 R. WANG and 31. D. MERZ

4. Conclusions 1. We have established a correlation of crystalline polymorphism with the thermal

2. This correlation is described by the relationship stability of noncrystalline solids for elements between group numbers 7b and 3a.

N P F - 1 T - rc - Npp + 1 + (6 - ’

where T,, is the reduced crystallization temperature (= T,/T,; T , and T , are crys- tallization and melting temperature, respectively). This relationship is indicative of the presence of polymorphic bonding in elemental noncrystalline solids.

3. We found that metallic elements uniquely show two ranges of thermal stability, a low thermal stability range with T,, less than 0.07 and a high thermal stability range with T,, between 0.1 and 0.3. The high stability range correlated with elemental poly- morphism.

4. Metallic elemental noncrystalline solids that have low thermal stabilities are thought to have the Bernal random close-packed structure.

5. We propose that the structure of the high stability metallic elemental noncrystal- line solids is composed of polymorphic bonding induced by the presence of impurity atoms.

Achmowledgement

This work has been supported by the Division of Physical Research, U.S. Energy Research and Development Administration.

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(Received July 30, 1976)